- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / llpx / llsx.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/llsx.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/llsx.etc
new file mode 100644 (file)
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/lazysn_6.ma".
+include "basic_2/substitution/lleq.ma".
+include "basic_2/reduction/llpx.ma".
+
+(* LAZY SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS *****************)
+
+definition llsx: ∀h. sd h → relation4 ynat term genv lenv ≝
+                 λh,g,d,T,G. SN … (llpx h g G d T) (lleq d T).
+
+interpretation
+   "lazy extended strong normalization (local environment)"
+   'LazySN h g d T G L = (llsx h g T d G L).
+
+(* Basic eliminators ********************************************************)
+
+lemma llsx_ind: ∀h,g,G,T,d. ∀R:predicate lenv.
+                (∀L1. G ⊢ ⋕⬊*[h, g, T, d] L1 →
+                      (∀L2. ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L2 → (L1 ⋕[T, d] L2 → ⊥) → R L2) →
+                      R L1
+                ) →
+                ∀L. G ⊢ ⋕⬊*[h, g, T, d] L → R L.
+#h #g #G #T #d #R #H0 #L1 #H elim H -L1
+/5 width=1 by lleq_sym, SN_intro/
+qed-.
+
+(* Basic properties *********************************************************)
+
+lemma llsx_intro: ∀h,g,G,L1,T,d.
+                  (∀L2. ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L2 → (L1 ⋕[T, d] L2 → ⊥) → G ⊢ ⋕⬊*[h, g, T, d] L2) →
+                  G ⊢ ⋕⬊*[h, g, T, d] L1.
+/5 width=1 by lleq_sym, SN_intro/ qed.
+
+lemma llsx_sort: ∀h,g,G,L,d,k. G ⊢ ⋕⬊*[h, g, ⋆k, d] L.
+#h #g #G #L1 #d #k @llsx_intro
+#L2 #HL12 #H elim H -H
+/3 width=6 by llpx_fwd_length, lleq_sort/
+qed.
+
+lemma llsx_gref: ∀h,g,G,L,d,p. G ⊢ ⋕⬊*[h, g, §p, d] L.
+#h #g #G #L1 #d #p @llsx_intro
+#L2 #HL12 #H elim H -H
+/3 width=6 by llpx_fwd_length, lleq_gref/
+qed.